library(tidyverse)
library(purrrlyr)
## install.packages("devtools")
## devtools::install_github("kleinschmidt/beliefupdatr", agrs="--preclean")
library(beliefupdatr)\[ \begin{align} p(c=\mathrm{b} | x) = \int \cdots \int & d\mu_b d\mu_p d\sigma^2_b d\sigma^2_p \\ & \frac{p(x | \mu_b, \sigma^2_p) p(c=b)}{p(x | \mu_b, \sigma^2_p) p(c=b) + p(x | \mu_p, \sigma^2_p) p(c=p)} \\ & p(\mu_b, \mu_p, \sigma^2_b, \sigma^2_p) \end{align} \]